Elizabeth Mowat is a former teacher of mathematics and a recent graduate of the doctoral program at the University of Alberta in the Department of Secondary Education. Research interests are complexity science, cognition in mathematics, and exponentiation. Her dissertation Making Connections: Network Theory, Embodied Mathematics, and Mathematical Understanding is available at http://hdl.handle.net/10048/853.

Brent Davis

Brent Davis is Professor and Distinguished Research Chair in Mathematics Education at the University of Calgary. His research is developed around the educational relevance of developments in the cognitive and complexity sciences, and he teaches courses at the undergraduate and graduate levels in curriculum studies, mathematics education, and educational change. Davis has published books and articles in the areas of mathematics learning and teaching, curriculum theory, teacher education, epistemology, and action research. His most recent book is Engaging Minds: Changing Teaching in Complex Times (2nd edition, 2008; co-authored with Dennis Sumara and Rebecca Luce-Kapler).

Abstract

Working from the premise that mathematics knowledge can be described as a complex unity, we develop the suggestion that network theory provides a useful frame for informing understandings of disciplinary knowledge and content learning for schooling. Specifically, we use network theory to analyze associations among mathematical concepts, focusing on their embodied nature and their reliance on metaphor. After describing some of the basic suppositions, we examine the structure of the network of metaphors that underlies embodied mathematics, the dynamics of this network, and the effect of these dynamics on mathematical understanding. Finally, implications for classroom teaching and curriculum are discussed. We conjecture that it is both instructive and important to use the network structure of mathematical knowledge to shed light on both cognition in mathematics and on mathematics education.